4 people can paint 7 walls in 45 minutes. How many minutes will it take for 6 people to paint 10 walls? Round to the nearest minute.
Solution: We know the following about the number of walls $w$ painted by $p$ people in $t$ minutes at a constant rate $r$ $w = r \cdot t \cdot p$ $\begin{align*}w &= 7\text{ walls}\\ p &= 4\text{ people}\\ t &= 45\text{ minutes}\end{align*}$ Substituting known values and solving for $r$ $r = \dfrac{w}{t \cdot p}= \dfrac{7}{45 \cdot 4} = \dfrac{7}{180}\text{ walls painted per minute per person}$ We can now calculate the amount of time to paint 10 walls with 6 people. $t = \dfrac{w}{r \cdot p} = \dfrac{10}{\dfrac{7}{180} \cdot 6} = \dfrac{10}{\dfrac{7}{30}} = \dfrac{300}{7}\text{ minutes}$ $= 42 \dfrac{6}{7}\text{ minutes}$ Round to the nearest minute: $t = 43\text{ minutes}$